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Chapter 10: Q. 4 (page 665)

A quiz question gives random samples of n=10observations from each of two Normally distributed populations. Tom uses a table of t distribution critical values and 9degrees of freedom to calculate a 95%confidence interval for the difference in the two population means. Janelle uses her calculator鈥檚 two-sample t interval with 16.87degrees of freedom to compute the 95%confidence interval. Assume that both students calculate the intervals correctly. Which of the following is true?

(a) Tom鈥檚 confidence interval is wider.

(b) Janelle鈥檚 confidence interval is wider.

(c) Both confidence intervals are the same.

(d) There is insufficient information to determine which confidence interval is wider.

(e) Janelle made a mistake; degrees of freedom have to be a whole number.

Short Answer

Expert verified

The true statement is option (a) Tom鈥檚 confidence interval is wider.

Step by step solution

01

Concept introduction

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution centered on the mean, indicating that data around the mean occur more frequently than data far from it.

02

Explanation

Janelle, on the other hand, employs more degrees of freedom than Tom.

A lower t*-value is associated with a higher degree of freedom.

A lower t*-value means a smaller margin of error and, as a result, a smaller confidence interval.

Then we know that Janelle's confidence interval is narrower than Tom's confidence interval, or Tom's confidence interval is wide than Janelle's confidence interval.

Thus the answer (a) is correct.

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Most popular questions from this chapter

At a baseball game, 42of 65randomly selected people report owning an iPod. At a rock concert occurring at the same time across town, 34of 52randomly selected people to report owning an iPod. A researcher wants to test the claim that the proportion of iPod owners at the two venues is different. A 90%confidence interval for the difference in population proportions is ( 0.154, 0.138). Which of the following gives the correct outcome of the researcher鈥檚 test of the claim?

(a) Since the confidence interval includes 0, the researcher can conclude that the proportion of iPod owners at the two venues is the same.

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(d) Since the confidence interval includes more negative than positive values, the researcher can conclude that a higher proportion of people at the rock concert own iPods than at the baseball game.

(e) The researcher cannot draw a conclusion about a claim without performing a significance test.

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